The sm (sm) was first introduced in [1]}'s seminal paper “College Admission and the Stability of Marriage". In an instance of sm we have two sets of agents, men and women (of equal number, henceforth \(n\) ), such that each man ranks every woman in strict preference order, and vice versa. An extension to sm, known as the smi (smi) allows each man (woman) to rank a subset of women (men). Let \(m\)  denote the total length of all preference lists.
